In episode 616, you can see Law cutting the entire island and Vergo with his Haki on full power in half, using only 'room' which is his Devil Fruit power, and it doesn't seem like Law was using Haki because his sword didn't turn black. But Zoro had to use Santoryu Ogi Three Thousand Worlds to cut Pica in half with Haki on all of his swords. Does that mean that Law is stronger than Zoro skill-wise?

Well, I think in the anime, the characters are much more stronger than normal buildings, etc. The doflamingo could cut many buildings in a single attack, but when he did same attack on law, he got wounded instead of getting cut in half. So, IMO, characters are too strong in one piece.
– berserkJul 30 '16 at 13:19

When Law cuts the island in half, wasn't he using his devil fruit to establish a 'room'?
– CybersonJul 30 '16 at 18:32

@Cyberson yes he was, sorry, i missed that part
– DragonJul 31 '16 at 5:08

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I'd argue no. Especially since Law has not yet (at least not in the cannon of the anime) defeated anyone without the use of his df. In addition to that Zoro has shown no form of rivalry with Law in spite of Law also being a swordsman. Throughout the series whenever Zoro sees anyone that may prove a rival or a fellow "I-want-to-be-the-greatest-swordsman" personality Zoro always jumps at the chance to test his skills. But never does with Law. Now Kinemon? That's another story...
– CallatJul 31 '16 at 15:19

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Laws powers are all about his Room. Anything in it he can manipulate at will with motion commands. The only thing implied that he can not cut is Haki and possibly Kaiorseki. Everything else isnt technically cut, but instead by the powers of his ope ope fruit, split.
– RyanAug 1 '16 at 2:52

1 Answer
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Well, this is rather an odd question as your are comparing apples with oranges. Let's recapitulate.

Law is using his Devil fruit power to cut through anything which reside inside his room. On the other hand, Zorro uses only his skill.

In episode 616, you can see Law cutting the entire island and vergo with his haki on full power in half only using 'room' which is his devil fruit power and it doesn't seem like Law was using Haki because his sword didn't turn black.

If you are asking whether Zorro could cut the entire Island like Law did, with his current set of skills, the answer is probably NO. As the OP already pointed out, Zorro had to gather a great amount of concentration in order to cut Pica in half, a feat which would be a piece of cake for someone able to cut an entire island in half.

Now for the speculation and deduction from what we've seen in the manga/anime. As it has been pointed out in the comments, Zorro is solely relying on his skills while Law on his devil fruit power. Zorro's goal is to become the greatest swordman in the world. He has dedicated his life to the sword in order to refine his skills indefinitely.He also has previously refused any tools or cheats in order to upgrade his sword technique, as seen in Chapter 301:

However, Law never shown such ambition or dedication to the sword. Therefore, it is safe to assume that in terms of skills alone, Zorro is far better than Law.

EDIT:

In the fight between Law and Vergo, Law seems to cut through Vergo's Haki with his DF powers alone, as his sword is not black as we have seen when Zorro uses it for example. Intuitively, one would think that a DF power is useless against Haki, which does not seem to be the case. Maybe Law's DF powers overpowers Vergo Haki?

This reminds me of when Luffy was using Buggy to protect himself from Mihawk's sword during the Whitebeard vs Marine war. Mihawk, being the best swordsman in the world, is an expert in Haki. Yet, he does not yield any damage to Buggy. Is this because he was not using it (Haki was not painted back then) or because Buggy's actual power is that he cannot be cut?

At one point you said that " in terms of skills alone, Zorro is far better than Law" but at the same time you said that "with current skills Zorro will not be able to cut one entire island ". Can you give some more explanation as if why he won't be able to cut one entire island ?
– Light YagamiAug 1 '16 at 12:30

@LightYagami About cutting the island, my answer was actually "probably no". Again, that uses some speculation from my part. As the OP stated, Zorro had to use a great amount of concentration and Haki in order to cut Pica into pieces. If he has to be very serious in order to cut Pica in half, then it is safe to safe than cutting an entire Island might be out of his reach
– solalitoAug 1 '16 at 12:43

@LightYagami The fact that Law was able to cut the island doesn't mean he has greater skills than Zorro because he used his Devil Fruit's power! Again, I pointed out that my answer is mostly speculation, based on what we've seen in the manga/anime.
– solalitoAug 1 '16 at 12:46

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Its true till now there is no theory which proves that Zorro can cut one entire island in single slash. So yeah its safe to assume that he won't be able to do it. I just read about Zorro all techniques in wiki and so far he manage to cut one large solid stone. Got it ! Thanks
– Light YagamiAug 1 '16 at 12:57

thanks for the answer but wouldn't it also take a lot of skill to cut vergo's haki (which was said to be one that Law was never able to cut) along with the entire island without haki? and didn't Law say somewhere in the anime/manga that his room has a limited size?
– DragonAug 2 '16 at 11:02